Week 25: Introduction to options — calls, puts, premium, intrinsic and time value

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1. Why This Is Important

For twelve weeks the course was about owning things. For the next six weeks it is about owning contracts on things. An option is not a share, not a bond, not an index — it is a piece of paper that says "if certain conditions hold at a certain date, money changes hands." That is a stranger object than it sounds, and the only way to get comfortable with the strategies in weeks 26-30 is to spend a week inside the contract itself.

You need this lesson for four concrete reasons.

(1) The vocabulary is dense, and almost every word is a small trap. "Premium" means three different things depending on context. "ITM" is not the same idea for a call as for a put. "Exercise" and "assignment" are the same event seen from two sides of the trade. Most retail blow-ups in options come from people who learned the strategy before they learned the vocabulary, and end up holding a position whose mechanics they cannot describe in one sentence. Spend the week on the words; the strategies are easy after.

**(2) Premium decomposition is the engine behind every option income strategy.* Every option price has two pieces — intrinsic value* (real, frozen, immune to time) and time value (a wasting asset). The covered calls and cash-secured puts of weeks 26-28 are *time-value harvesting* trades. If you cannot look at a quote and tell those two numbers apart, you cannot tell whether a strategy is paying you to take risk or taking risk for free. The decomposition image in this lesson is the single most important picture in the second half of the course.

**(3) The four basic positions are a coordinate system, not four trades.** Long call, short call, long put, short put. Every option strategy you will meet for the rest of your life is a combination of those four — a vertical spread is two of them, an iron condor is four, a covered call is one of them plus 100 shares of stock. Internalise the four payoff shapes once and the rest of options is bookkeeping.

**(4) This is foundation for the barbell, the tax stack, and the vol-tail-wags-dog mechanic.** The barbell holds long-dated calls on the safety end and uses short near-dated puts/calls on the income middle — both are option positions. The tax stack reaches for options because they let you reshape exposure without realising a sale. The vol-tail mechanic only makes sense once you understand that dealers hedge the options they sell, and that hedging flow moves the spot. Without this week, three pieces of the broader investing playbook remain abstract.

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2. What You Need to Know

2.1 An option is a contract — right on one side, obligation on the other

An option is a contract between two parties:

• A buyer (also "long" or "holder") who pays a premium in cash

up front, and in return receives a right.

• A seller (also "short" or "writer") who receives that premium,

and in return takes on an obligation.

The right and the obligation are exact mirrors. If the buyer chooses to use the right, the seller is forced to deliver. The whole edifice of options pricing is just the question *"how much should the buyer pay the seller for taking on that obligation?"*

There are exactly two flavours.

A call is the right to buy the underlying at a fixed price. You buy a call when you want upside exposure to the stock without putting up the full share price.

A put is the right to sell the underlying at a fixed price. You buy a put when you want a floor under the stock — protection, or a directional bet that it will fall.

A complete US-listed equity option is identified by five fields:

Underlying — the ticker (SPY, AAPL).

Expiration date — the last day the right can be exercised.

Strike price (K) — the fixed price at which the buy/sell

happens if the right is exercised.

Type — call or put.

Style — American or European (covered in §2.5).

A typical broker-screen quote: AAPL 16-Jan-2026 200 C @ 8.50 / 8.65. Read this as *"AAPL January-16-2026, $200 strike, call. Bid 8.50, ask 8.65."* That single line contains all five identifiers plus the live market for the contract.

2.2 The contract is for 100 shares — and the premium is per share

The most common stumble for a new options trader is the units. US listed equity options are standardised at 100 shares per contract. The premium is quoted per share, not per contract. To get the dollar amount that actually moves in your account, multiply by 100.

For the AAPL example above, "ask 8.65" means $865 per contract ($8.65 x 100). One contract gives the buyer the right to buy 100 shares of AAPL at $200 each — a $20,000 notional position — for an upfront payment of $865. That is the leverage.

Two consequences fall out of the 100-share spec:

• Anything below $20,000 of stock notional and you can't buy/sell

fractional contracts. There is no half-contract. If the strategy needs a 50-share hedge, options are not the right tool.

• Account size matters. A cash-secured put at the $200 strike

ties up $20,000 of collateral. If your whole account is $30,000, this strategy lives in larger names like SPY or QQQ where you can go far enough out-of-the-money to make a $5,000 collateral commit reasonable.

The 100-share unit is also why every example in this course quotes position size in contracts rather than dollars — saying "sell 1 $200 SPY put" is unambiguous; saying "sell $20,000 worth" requires arithmetic at every step.

2.3 Moneyness — ITM, ATM, OTM

The relationship between the strike K and the current spot S defines the option's moneyness.

For a call, "moneyness" measures how far above the strike the spot is — i.e. how much real value the right contains right now:

Term	Condition (call)	Intrinsic value
In-the-money (ITM)	S > K	S - K
At-the-money (ATM)	S ~= K	~0
Out-of-the-money (OTM)	S < K	0

For a put, the inequalities flip — the right is to sell at K, which is valuable when spot is below K:

Term	Condition (put)	Intrinsic value
In-the-money (ITM)	S < K	K - S
At-the-money (ATM)	S ~= K	~0
Out-of-the-money (OTM)	S > K	0

A call ITM is a put OTM at the same strike, and vice versa. For a call at K=100 with spot at S=110: the call is $10 ITM (intrinsic value $10), and the corresponding put at the same strike is $10 OTM (intrinsic value 0). They are sides of the same coin.

Three practical observations.

ATM options have the most time value. They are the closest to the boundary between worth-something and worth-nothing, so the "insurance premium" the seller charges for being on the wrong side of a small move is largest there. For premium-sellers (weeks 26-28), ATM contracts pay the most absolute premium per day; for tail-hedge buyers (week 29), OTM contracts pay the most leverage per dollar of premium.

Deep ITM options behave almost like the stock itself (delta near 1 for calls, near -1 for puts) — they are leverage substitutes more than they are options. Deep OTM options behave almost like lottery tickets — most expire worthless, a few pay 5-50x when the tail event happens.

The "moneyness" axis is one of the two main axes of the option chain (the other is expiry). Every screenshot of an options chain in this course is a 2D grid: strikes down, expirations across.

2.4 Premium = intrinsic value + time value

Every option premium decomposes into exactly two pieces.

Intrinsic value is what you would receive if you exercised the option right now. It is the moneyness, in dollars. It cannot be negative (you would simply not exercise) — it is max(S - K, 0) for a call, max(K - S, 0) for a put.

Time value (also called extrinsic value) is everything else. It is the premium paid over the intrinsic value, and it compensates the seller for the risk that, between now and expiry, the option ends up further in-the-money than it is today. Time value depends on three things:

Time to expiry (DTE). More days until expiry = more chances

for the spot to move, so more time value. Time value decays toward zero as expiry approaches; the decay accelerates in the final 2-3 weeks (the "theta wall").

Implied volatility (IV). A higher expected move = a wider

future range = more time value. IV is the option market's forecast of the underlying's volatility through expiry.

Risk-free interest rate. Modest effect — the call is a

deferred-purchase, so higher rates make a call slightly more valuable; the put is a deferred-sale, so higher rates make a put slightly less valuable. This effect is usually small for front-month options.

The image below shows premium decomposition for a 30-day call at strike $100 with sigma=20% and r=4%, across spots from $50 to $150. The shaded intrinsic area is the linear max(S - K, 0) payoff; the shaded time value sits on top. Notice how time value is largest at the strike and tapers to near-zero at both ends.

The reason ATM time value peaks is symmetry. At spot = strike, the option has equal odds of expiring on either side of the strike, so the seller is taking the most actuarial uncertainty per dollar of premium and charges accordingly. Far ITM, the option is "almost certainly going to be exercised" — its price is mostly real intrinsic, with a thin wrapper of optionality. Far OTM, the option is "almost certainly going to expire worthless" — its price is a small lottery-ticket wrapper with no intrinsic.

This decomposition is the single most useful framing in this whole half of the course. Premium-selling strategies (weeks 26, 27, 28) make money when the time-value piece decays to zero. Premium-buying strategies (week 29 protective puts, week 30 long calls as substitutes) pay for that time value up front and need the spot to move enough to recover it.

2.5 Expiry — weekly, monthly, LEAPS, and American vs European

US listed equity options come in three calendar flavours:

• Weekly options ("weeklies") expire every Friday. Most

high-volume names (SPY, QQQ, AAPL, NVDA, etc.) have weeklies for every Friday in the next 4-8 weeks. Weeklies trade huge volumes and are the workhorse for short-dated hedging and gamma trades.

• Monthly options expire on the third Friday of the month.

This is the historical default; "monthlies" have the deepest open interest, the tightest bid-ask, and the most strikes listed. The 30-45 DTE monthly is the canonical "premium-sell" contract for retail.

• LEAPS (Long-term Equity AnticiPation Securities) are

options with more than 9 months to expiry. They go out as far as ~2.5 years on the most active names. LEAPS are the building block for the long-call-as-stock-substitute trades on the safe end of Horace's barbell — they let you control 100 shares for ~15-25% of the share price, with capped downside, and let the position age into long-term-capital-gains tax treatment.

Two exercise styles matter for retail:

• American style. The right can be exercised on any business

day from purchase up to and including expiry. All US listed equity options (AAPL, SPY, QQQ, etc.) are American-style.

• European style. The right can only be exercised *on the

expiry date itself. US listed cash-settled index* options (SPX, NDX, RUT) are European-style.

For most retail option strategies, the practical difference is small because early exercise is almost always suboptimal — exercising early throws away the remaining time value. The two cases where American-style early exercise actually happens: deep-ITM puts (the holder gets cash earlier) and the day before a large dividend on a deep-ITM call (the holder captures the dividend). These edge cases matter for the seller of those contracts — you can be assigned unexpectedly. We treat them as they come up in week 27.

Settlement is also worth knowing. Equity options settle physically: exercise of an AAPL call delivers 100 shares of AAPL. Index options settle in cash: exercise of an SPX put pays out the difference between strike and settlement value, no shares change hands. This matters when sizing — a deep-ITM SPX put pays cash on Friday; a deep-ITM SPY put delivers a short stock position that has to be closed by Monday.

2.6 The four basic positions

Strip away all the strategy names and there are exactly four positions a retail account can take in a single contract: long call, short call, long put, short put. Every strategy in weeks 26-30 is either one of these four or a combination of them with the underlying stock.

The image below is the 2x2 grid of payoff diagrams at expiration for those four. Each panel shows P&L per share as a function of spot at expiry, with breakeven, max profit, and max loss annotated.

A one-line summary of each:

Long call. Pay premium c for the right to buy at K. Max loss = c (option expires worthless). Breakeven at expiry: K + c. Upside unbounded above breakeven. Use case: directional bullish bet with capped loss; LEAPS-as-stock-substitute on the safe end of the barbell.

Short call. Receive premium c, take on obligation to sell at K. Max gain = c. Breakeven at expiry: K + c. Loss unbounded above breakeven. Naked short calls are dangerous. Covered calls (with 100 shares as collateral, week 27) cap the loss at "the unrealised gain you didn't get to keep" — bounded, not unbounded.

Long put. Pay premium p for the right to sell at K. Max loss = p. Breakeven at expiry: K - p. Max gain = K - p (spot goes to zero). Use case: portfolio insurance (week 29), bearish directional bet, vol-spike trades.

Short put. Receive premium p, take on obligation to buy at K. Max gain = p. Breakeven at expiry: K - p. Max loss = K - p (spot goes to zero — the seller still has to buy at K). Naked short puts are dangerous in size; cash-secured puts (week 28) have the full collateral set aside and the loss is bounded — and identical, in P&L terms, to a limit-buy order at K filled at

K - p. This is one of the most useful retail option positions.

The four positions plus the underlying stock (long shares, short shares) give six primitives. Every named strategy you will see — covered call, cash-secured put, vertical spread, iron condor, collar, straddle, strangle, calendar — is a combination of those six. Memorise the four payoff shapes; the rest is bookkeeping.

2.7 Where this lesson fits — barbell, tax, and the vol tail

Three pieces of Horace's broader investing playbook lean directly on the foundation laid this week.

The barbell. The safe end of Horace's barbell uses long-dated, deep-ITM calls (LEAPS) as a capital-efficient share substitute — you control the upside of 100 shares with 20% of the capital, the loss is capped at the premium, and you free up cash for the speculative end. The income middle (the L2 sleeve) writes short calls and short puts against quality names to harvest time value. Both ends of the barbell are options; the lesson this week is the dictionary that lets you read either end.

Options as a tax tool. The covered call lets you reduce delta on a winner without selling the share — the lot keeps aging toward long-term-capital-gains treatment, no taxable event, exposure shifts. The cash-secured put lets you build a position at a chosen entry over multiple expiries, with each unfilled expiration banking premium that lowers the eventual cost basis. Both depend on the time-value/intrinsic-value split from §2.4 — the part being harvested is the time value.

The option tail wags the equity dog. Dealers who sell options to retail and institutions hedge their books in the underlying stock. Their hedge depends on the option's delta, which itself depends on spot, strike, IV, and time. When spot moves, deltas move, dealer hedges move — and that mechanical hedging flow moves the spot further. The 2021 GameStop squeeze was that mechanism running in reverse: retail bought calls, dealers were forced to buy spot to hedge, the spot ran, and the rally was self-reinforcing until the calls expired. We will not work the math of dealer hedging in this course, but you cannot understand modern US equity microstructure without knowing that the option chain is no longer a sideshow to the spot tape. It is increasingly the cause of the spot tape.

The interactive lab for this week (course/interactive/week25_option_explorer.html) lets you pick any of the four positions, drag the strike, expiry, volatility, rate, and spot sliders, and watch the premium decomposition update in real time alongside the at-expiry payoff. Spend twenty minutes in it before reading week 26. Six weeks of strategy material rest on those five sliders.

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3. Common Misconceptions

"Buying calls is how you get rich." Calls are time-decaying

instruments. The median outcome of buying an OTM front-month call is total loss of the premium. Single-call buyers historically underperform — sometimes by enormous margins — buy-and-hold investors in the same name. Calls are tools, not lottery tickets, and the cases where they make sense (LEAPS substitutes, targeted event trades) are narrow.

"Options are too risky for retail investors." Naked short

options are risky for retail. Long calls, long puts, covered calls, and cash-secured puts have bounded, fully-knowable worst cases at the moment you place the trade. The biggest risk in options is the gap between what the strategy actually does and what the trader thinks it does — fix that gap and the risk profile is no scarier than the stock itself.

"The premium is the cost of the option." The premium is the

cost only if you're the buyer. If you're the seller, the premium is your income — and the cost is the obligation you took on. Every dollar of premium has two signs depending on which side of the trade you're sitting on. Half the lesson is noticing that.

"Out-of-the-money options are 'safer' because they're cheap."

Cheap and safe are different. A $0.10 OTM call is cheap in absolute dollars, but it has a ~95% probability of expiring worthless. Buying a basket of cheap OTM calls is one of the most consistent ways retail traders bleed capital. Cheap measures dollars per contract; safe measures probability of loss.

"At-the-money options have no value because intrinsic is zero."

ATM options are all time value and time value is largest at the strike. An ATM 30-day option on SPY is one of the most valuable single contracts in the chain — not despite zero intrinsic, because of maximum time value. Don't confuse "no intrinsic value" with "no value."

"Exercising the option is what makes you the money." For

retail traders, exercising is almost always wrong. Exercising throws away the remaining time value; instead you *sell to close* the option in the market and capture both intrinsic and time value. Exercise is a settlement event handled by the broker on the few cases where it's optimal. Beginners who reflexively exercise ITM longs leave money on the table.

**"American options are more valuable because you can exercise

any time."** Slightly more valuable in theory; in practice essentially identical to European on equity. The American-style premium is real for deep-ITM puts and dividend-day calls; for most front-month at- or near-the-money positions, it is a rounding error.

"One contract = one share." One contract = 100 shares. The

single most common rookie mistake is reading "premium 8.50" as "$8.50 to buy" rather than "$850 to buy." Always multiply.

"LEAPS are basically the same as monthly options, just longer."

LEAPS behave very differently. Most of their value is intrinsic (or near-intrinsic with low theta). Vega is the dominant Greek, not theta. They are leverage instruments far more than they are pure optionality. Strategies that work with monthlies (premium-selling, gamma scalping) often don't work with LEAPS, and vice versa.

"If I learn the Greeks I'll understand options." Backwards.

The Greeks are calculus on top of the four payoff shapes; if the four shapes aren't second nature, the Greeks are incomprehensible. Learn the four positions first. Greeks come in week 26 onward, in context, when they matter.

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4. Q&A Section

**Q1: I keep getting confused by "long" and "short" in options. Can you give me a one-line rule?**

A: *Long = paid the premium up-front and now hold a right. Short = received the premium and now hold an obligation.* Long anything (call or put) means you are the buyer; short anything means you are the seller/writer. The direction of the underlying view is independent — "long the stock" goes up means up; "long a put" goes up means the stock went down. Don't merge the two dimensions.

**Q2: Why do options expire? Wouldn't they be more useful if they didn't?**

A: Without expiry there would be no time-value premium and no seller would write contracts at a positive price. Expiry is what turns an option from a permanent right (which would be priceless) into a finite, tradeable contract. The seller is being paid for the finite window of risk; without that window there is nothing to be paid for.

Q3: How do I read a chain quote like AAPL 1/16/26 200C 8.50/8.65?

A: Underlying = AAPL; expiry = January 16, 2026; strike = $200; type = Call; bid = $8.50, ask = $8.65 per share. To trade one contract the buyer pays the ask x 100 = $865; the seller receives the bid x 100 = $850. The $15 spread is the market-maker's compensation for quoting both sides.

Q4: Why does ATM have the most time value?

A: Because at the strike, the option has equal odds of expiring on either side of the strike, so the *uncertainty per dollar of premium* is largest there. Move spot $20 above K — the call is now "almost certainly exercised" and the time-value wrapper shrinks. Move spot $20 below K — the call is now "almost certainly worthless" and the time-value wrapper shrinks. The peak is at the strike for the same reason a flipped coin's outcome is most uncertain when it's spinning.

Q5: Should I exercise or sell my in-the-money long option?

A: Almost always sell, never exercise. Exercising throws away the remaining time value; selling captures both intrinsic and time value. The only retail exception is if you actually want the 100 shares of stock and the option is past the ex-dividend date or nearly at expiry — and even then, "exercise + immediately sell" and "sell the option" net to roughly the same dollars after spreads.

Q6: What does it mean to "be assigned"?

A: Assignment is the seller-side event where the buyer chose to exercise. As the seller, you are forced to deliver the underlying (short call -> forced to sell 100 shares; short put -> forced to buy 100 shares). Assignment can happen any business day for American- style equity options, but in practice almost always at or near expiry. Cash-secured puts and covered calls treat assignment as the intended outcome, not a failure mode.

Q7: Can I lose more than I put in?

A: It depends on the position. Long calls and long puts: max loss is the premium paid — full stop. Short covered calls: max loss is "the upside you didn't capture" — bounded. Short cash-secured puts: max loss is (strike x 100) - premium, fully collateralised. Naked short calls: theoretically unlimited (don't do it without deep training and clear risk limits). Naked short puts: bounded but larger than the collateral typically posted on margin (also avoid without training).

Q8: How is implied volatility different from realised volatility?

A: Realised vol = how much the stock has actually moved over a recent window (a backward-looking measurement). Implied vol = the volatility figure that, plugged into the Black-Scholes formula, returns the option's current market price (a forward-looking forecast embedded in the price). When IV > recent realised, the options market expects movement to pick up; when IV < realised, the market expects calm to return. The gap between the two is one of the oldest signals in derivatives.

Q9: Why 30-45 days to expiry for retail premium-selling?

A: Theta — the rate of time-value decay — is fastest in the 21-45 DTE band. Shorter than 21 days and the daily premium is small per contract for the capital tied up; longer than 45 days and the daily decay slows down meaningfully and you're locking up collateral for a smaller daily yield. The 30-45 DTE band has been the empirical sweet spot for retail premium-sellers for decades; SPY weeklies and 30-day monthlies are the workhorse contracts.

Q10: What's the smallest options account that makes sense?

A: Roughly $25,000-$50,000 to do cash-secured puts and covered calls on liquid US ETFs (SPY, QQQ, IWM) with one or two contracts at a time. Below that, the 100-share contract size forces you into penny names where the bid-ask spread eats the premium. Below $10,000, options are not the right tool — stick to share-buying discipline. The contracts are not scaled for very small accounts.

Q11: I've heard "options trading is zero-sum." Is that true?

A: Yes, in dollars before fees. Every dollar a buyer makes is a dollar a seller loses, and vice versa, for any single contract. This is different from the stock market, which is positive-sum (companies generate cash flows). In options, you are negotiating who takes which slice of an existing risk. After fees and bid-ask spreads, options are negative-sum. This is why the strategy matters more than the prediction — being on the right side of the asymmetry beats being right about direction.

**Q12: When does this lesson stop being theoretical and start being useful?**

A: Week 26. Every concept introduced this week — premium = intrinsic + time, the four positions, ITM/ATM/OTM, weekly vs monthly vs LEAPS — gets used immediately in week 26 (options as limit orders), week 27 (covered calls), week 28 (cash-secured puts), week 29 (protective puts), week 30 (LEAPS-as-stock). This is the dictionary week. Keep the interactive open in another tab while you read the next five.